Parametric Amplification of a Quantum Pulse

Quantum states of light are the key ingredients for quantum technologies such as quantum sensing, communication, and certain computation platforms. It has long been known that there is a deep connection between nonlinear physics and quantum optics, and that creation and manipulation of quantum states of light requires nonlinearity. In addition, most of the interesting phenomena in nonlinear optics are tightly connected to the inherently multimode nature of light, such as the generation of new frequencies via nonlinear processes. Nevertheless, the multimode aspects of nonlinearities in quantum optics have received only little attention.

In this work, we begin to solve this problem by finding how a quantum pulse transforms under second order Hamiltoians, taking into account parametric amplificatio, dispersion, frequency conversion and other nonlinear effects. We found one quite suprising result: If you come into a parametric amplifier with a single mode pulse, then the quantum state outside may contain infinite temporal modes, but the information on the input quantum pulse will always be kept in at most two. This allows us to solve the problem and answer what is the multimode state at the output.

Check out our paper here